Publications and Preprints
Publications:

Regularized inner products of meromorphic modular forms and higher Green's functions (with Kathrin Bringmann and AnnaMarie von Pippich)
Commun. Contemp. Math, accepted for publication.

On divisors of modular forms (with Kathrin Bringmann, Steffen Löbrich, Ken Ono, and Larry Rolen)
Adv. Math. 329 (2018), 541554.

Almost universal ternary sums of polygonal numbers (with Anna Haensch)
Research in Number Theory 4:4 (2018), 122.

Regularized inner products and weakly holomorphic Hecke eigenforms (with Kathrin Bringmann)
Journal of Physics A: Mathematical and Theoretical 51 (2018) 044001.
 The BruinierFunke pairing and the orthogonal complement of unary theta functions (with Siu Hang Man) (local version)
in Bruinier, J., Kohnen, W. (Eds.), "Lfunctions and automorphic forms",
Contributions in mathematical and computational sciences 10 (2017), Springer, 139157.

On the AndrewsZagier asymptotics for partitions without sequences (alternative link here) (with Kathrin Bringmann, Dan Parry, and Rob Rhoades)
Adv. Math. 309 (2017), 436451.
 Analogues of the RamanujanMordell Theorem (with Shaun Cooper and Dongxi Ye)
J. Math. Anal. Appl. 446 (2017), 568579.
 On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring (with King Cheong Fung)
Math. Comp. 87 (2017), 501514.

Polar harmonic Maass forms and their applications (with Kathrin Bringmann)
Abh. Math. Sem. Univ. Hamburg 86 (2016), 213233.

A problem of Petersson about weight 0 meromorphic modular forms (with Kathrin Bringmann)
Res. Math. Sci. 3:24 (2016), 131.
 Ramanujan and coefficients of meromorphic modular forms (with Kathrin Bringmann)
J. Math. Pures Appl. 107 (2017), 100122.
 Explicit congruences for mock modular forms (with Matthias Waldherr)
J. Number Theory 166 (2016), 118.

Halfintegral weight padic coupling of weakly holomorphic and holomorphic modular forms
(with Kathrin Bringmann and Pavel Guerzhoy)
Research in Number Theory 1:26 (2015), 113.

On cycle integrals of weakly holomorphic modular forms (with Kathrin Bringmann and Pavel Guerzhoy)
Math. Proc. Cambridge Philos. Soc. 158 (2015), 439449.

Modular local polynomials (with Kathrin Bringmann)
Math. Res. Lett. 23 (2016), 973986.

Locally harmonic Maass forms and the kernel of the Shintani lift (local version) (with Kathrin Bringmann and Winfried Kohnen)
Int. Math. Res. Not. 2015 (2015), 31853224.

Shintani lifts and fractional derivatives for harmonic weak Maass forms (with Kathrin Bringmann and Pavel Guerzhoy)
Adv. Math. 255 (2014), 641671.

Sums of class numbers and mixed mock modular forms (with Kathrin Bringmann),
Math. Proc. Cambridge Philos. Soc., accepted for publication.

Theta lifts and local Maass forms (with Kathrin Bringmann and Maryna Viazovska),
Math. Res. Lett. 20 (2013), 213234.

On a completed generating function of locally harmonic Maass forms (with Kathrin Bringmann and Sander Zwegers),
Compositio Math. 150 (2014), 749762, doi:10.1112/S0010437X13007719.
 Second order cusp forms and mixed mock modular forms (with Kathrin Bringmann),
Ramanujan J., Special issue in honor of Ismail and Stanton, 31 (2013), 147161, doi: 10.1007/s1113901294084.
 Duality and differential operators for harmonic Maass forms (with Kathrin Bringmann and Robert Rhoades)
Dev. Math. 28, Special volume in memory of Leon Ehrenpreis: From Fourier analysis and number theory to radon transforms and geometry (2013), 85106, doi: 10.1007/9781461440758_6.
 Inequalities for full rank differences of 2marked Durfee symbols (with Kathrin Bringmann)
J. Combin. Theory Ser. A 119 (2012), 483501.
 The triangular theorem of eight and representation by quadratic polynomials (with Wieb Bosma),
Proc. Amer. Math. Soc. 141 (2013), 14731486.
 Faber polynomials and Poincaré series,
Math. Res. Lett. 18, no. 4 (2011), 591611.
 Mock modular forms as $p$adic modular forms (with Kathrin Bringmann and Pavel Guerzhoy),
Trans. Amer. Math. Soc. 364 (2012), 23932410.
 Equidistribution of Heegner Points and Ternary Quadratic Forms (with Dimitar Jetchev),
Math. Ann. 350, no. 3 (2011), 501532.
 The aliquot constant (with Wieb Bosma),
Q. J. Math 63, no. 2 (2012), 309323.
 Representing sets with sums of triangular numbers,
Int. Math. Res. Not. 2009, no. 17 (2009), 32643285, doi:10.1093/imrn/rnp053.
 On almost universal mixed sums of squares and triangular numbers (with ZhiWei Sun),
Trans. Amer. Math. Soc. 362 (2010), 64256455.
 Multiplicative $q$hypergeometric series arising from real quadratic fields (with Kathrin Bringmann),
Trans. Amer. Math. Soc. 363 (2011), 21912209.
 Inequalities for differences of Dyson's rank for all odd moduli (with Kathrin Bringmann),
Math. Res. Lett. 17, no. 5 (2010), 927942.
 New identities involving sums of the tails related to real quadratic fields (with Kathrin Bringmann),
Special issue of the Ramanujan J. in honor of G.E. Andrews's 70th birthday, The Ramanujan J. 23 (2010), 243251.
 CM liftings of supersingular elliptic curves,
J. Théor. Nombres Bordeaux 21, no. 3 (2009), 635663.
 Representations of integers by ternary quadratic forms,
Int. J. Number Theory 6, no. 1 (2010), 127158.
 On simultaneous $s$cores/$t$cores (with David Aukerman and Lawrence Sze),
Discrete Math. 309 (2009), 27122720.
 On two conjectures about mixed sums of squares and triangular numbers,
J. Comb. Number Theory 1, no. 1 (2009), 7790.
 Sums of triangular numbers and $t$core partitions,
J. Comb. Number Theory 1, no. 1 (2009), 5964.
 On the boundary behaviour of automorphic forms (with Kathrin Bringmann and Winfried Kohnen)
Int. J. Number Theory 2, no. 2 (2006), 187194.
Preprints:
 Central Lvalues of elliptic curves and local polynomials (with Stephan Ehlen, Pavel Guerzhoy, and Larry Rolen)
submitted for publication.
 Universal sums of mgonal numbers (with Jingbo Liu)
submitted for publication.

Differential operators on polar harmonic Maass forms and elliptic
duality (with Kathrin Bringmann and Paul Jenkins)
submitted for publication.

Ramanujanlike formulas for Fourier coefficients of all meromorphic cusp forms (with Kathrin Bringmann)
submitted for publication.
Expository notes/survey papers:

Regularized Petersson inner products for meromorphic modular forms
Proceedings of RIMS (Surikaisekikenkyusho 2036) Kokyuroku conference "Automorphic forms, automorphic Lfunctions, and related topics" held at RIMS in February, 2016, (2017), 2030.

Topical review: Number theoretic generalization of the Monster denominator formula (with Kathrin Bringmann, Steffen Löbrich, Ken Ono, and Larry Rolen)
Journal of Physics A: Mathematical and Theoretical 50 (2017) 473001.

Polar harmonic Maass forms
Book chapter in "Encyclopedia of Srinivasa Ramanujan and His Mathematics", 3 pages, 2017.

An algebraic and analytic approach to spinor exceptional behavior in translated lattices (with Anna Haensch), Conference Proceedings of the 3rd Building Bridges Workshop 11—22 July, 2016, AMS Contemporary Mathematics series, to appear.

The Monster denominator formula
Book chapter in "Encyclopedia of Srinivasa Ramanujan and His Mathematics", in preparation.